It was reported this week that China's sovereign wealth fund is about to receive new capital from the government, adding billions of dollars annually to its already impressive wallet. As China's economic power continues to grow and countries around the world compete for Chinese investment, the question facing developed countries is not so much what happens when China rules the world, as what will be the impact when China owns the world?

The China Investment Corporation was set up in 2007 to invest some of the $3tn in foreign exchange reserves that have accumulated through trade surpluses – fuelled in part, critics would say, by an artificially depressed exchange rate. It is currently the world's fourth largest sovereign wealth fund but is growing fast as the Chinese government pursues its twin goals of securing raw materials and energy, and reducing its holdings of US treasury bonds – no longer seen by Beijing as future-proof.

Until 2000 China's investments outside Asia were small and largely aimed at energy and natural resources in Latin America and Africa. But now China is on a spending spree, buying into mining interests from Australia to Canada and looking for acquisitions that might give them technology, major brands or market access.

In addition a host of other Chinese companies have moved into Europe and the US. Luxury textiles and vineyards in Italy, electronics manufacturers in France, engineering in Germany and car manufacturers in Britain are only some of China's purchases. All are harmless enough; but as the writer Richard McGregor describes in his recent book on the Chinese Communist party, every significant Chinese company has a shadow party structure inside it. Before we sell the entire farm, should we not be clearer about who exactly is buying it?

Britain, one of the world's most open economies, has assiduously courted Chinese investment and now boasts more than 400 Chinese companies and 40% of Chinese inward investment to Europe. China is still a relatively small investor in the US and in Europe, but as both struggle to escape recession, the increasing pace of Chinese deals makes McGregor's question more salient: should China be regarded as just another country?

Right now, politicians and officials are tiptoeing towards a decision on the Chinese telecoms giant Huawei's offer of discounted mobile telephony for the London underground. The deal is described as "sensitive" in official circles, because Huawei exemplifies the suspicion that dogs China's industrial and commercial giants around the world. Ren Zhengfei, who founded the company in 1988, is a former People's Liberation Army officer, Huawei's corporate structure is opaque, and, as a key operator in Chinese telecoms, it has a close relationship with the government.

In the US, three Huawei deals have been blocked by the US committee on foreign investment. Huawei's opponents insist that ties to the PLA remain, despite company denials. China's policy of owning 50% of any "pillar" industry is enough to ensure continuing hostile scrutiny. And the US is not alone. In 2009, Australia, which has extremely close economic ties to China, invoked national security to disallow China's Minmetals group's attempted $1.8bn purchase of OZ Minerals on the grounds that the key asset – the Prominent Hill mine – was close to the Woomera weapons testing range.

China itself bans foreign investment in any military or national security sector and restricts it in other key areas: this has killed off some steel and construction sector deals and, bizarrely, Coca-Cola's bid for China's biggest juice maker. In February China set up its own mechanism for scrutinising foreign bids under national security rules. Britain has no similar mechanism. Perhaps it should learn from the Chinese.